Multi-tap decision feed-forward equalizer with precursor and postcursor taps

ABSTRACT

A multi-tap Differential Feedforward Equalizer (DFFE) configuration with both precursor and postcursor taps is provided. The DFFE has reduced noise and/or crosstalk characteristics when compared to a Feedforward Equalizer (FFE) since DFFE uses decision outputs of slicers as inputs to a finite impulse response (FIR) unlike FFE which uses actual analog signal inputs. The digital outputs of the tentative decision slicers are multiplied with tap coefficients to reduce noise. Further, since digital outputs are used as the multiplier inputs, the multipliers effectively work as adders which are less complex to implement. The decisions at the outputs of the tentative decision slicers are tentative and are used in a FIR filter to equalize the signal; the equalized signal may be provided as input to the next stage slicers. The bit-error-rate (BER) of the final stage decisions are lower or better than the BER of the previous stage tentative decisions.

CROSS-REFERENCE TO RELATED APPLICATION(S)

This application is a continuation of U.S. patent application Ser. No.17/164,325, filed on Feb. 1, 2021, which is a continuation of U.S.patent application Ser. No. 16/741,099, filed on Jan. 13, 2020, nowissued as U.S. Pat. No. 10,911,272 on Feb. 2, 2021, which claims thebenefit of U.S. Provisional Application No. 62/799,316 filed on Jan. 31,2019, the entire disclosures of which are hereby incorporated byreference.

BACKGROUND

Feedforward Equalizers (FFE) and Decision Feedback Equalizers (DFE) areamong the most common equalizers used in state of the art SerDesreceivers to compensate for Inter-Symbol Interference (ISI). Bothequalizers have their respective advantages and disadvantages. FFE hasthe ability to correct both precursor and postcursor ISI but it tends toamplify noise and crosstalk as well. DFE corrects postcursor ISI anddoes not boost noise in the process but it lacks the ability to correctprecursor ISI. DFE is a powerful equalizer for postcursor ISI correctionbut it suffers from error propagation that FFE does not. For DSP basedSerDes, a parallel data path realization of both these equalizers isrequired and FFE lends itself well for such implementations whereas DFEdoes not as its complexity increases exponentially with number for taps.Even though DFE is preferred over FFE due to its inherent ability to notamplify noise, it is not practical to implement it to correct postcursorISI beyond the first few taps. As such, most DSP SerDes receivers employmultiple taps of FFE for both precursor and postcursor ISI correctionfollowed by just one or two taps of DFE for postcursor correction.

BRIEF DESCRIPTION OF THE DRAWINGS

Aspects of the present disclosure are best understood from the followingdetailed description when read with the accompanying figures. It isnoted that, in accordance with the standard practice in the industry,various features are not drawn to scale. In fact, the dimensions of thevarious features may be arbitrarily increased or reduced for clarity ofdiscussion.

FIG. 1 depicts a block diagram of a communication system in accordancewith examples of the present disclosure.

FIG. 2 depicts a block diagram of a SerDes receiver architecture inaccordance with examples of the present disclosure.

FIG. 3 depicts an example signal illustrating locked, early, and lateclock conditions in accordance with examples of the present disclosure.

FIGS. 4A-4C depict example waveforms identifying precursor, cursor, andpostcursor locations in accordance with examples of the presentdisclosure.

FIG. 5. depicts a block diagram of a SerDes receiver architecture inaccordance with examples of the present disclosure.

FIG. 6 depicts a block diagram of a Feedforward Equalizer (FFE) with mPrecursor and n Postcursor taps in accordance with examples of thepresent disclosure.

FIGS. 7A-7C depict block diagrams of a Decision Feedback Equalizer (DFE)in accordance with examples of the present disclosure.

FIG. 8 depicts a block diagram of a single stage multi-tap DecisionFeedforward Equalizer (DFFE) in accordance with examples of the presentdisclosure.

FIG. 9 depicts a conceptual block diagram of a DFFE in accordance withexamples of the present disclosure.

FIG. 10 depicts a conceptual block diagram of a two-stage DFFE inaccordance with examples of the present disclosure.

FIG. 11 depicts a linear model of an ideal feedback equalizer inaccordance with examples of the present disclosure.

FIG. 12 depicts a linear model of a DFFE in accordance with examples ofthe present disclosure.

FIG. 13 depicts a linear model of a two-stage DFFE in accordance withexamples of the present disclosure.

FIG. 14 depicts a signal stage DFFE for cascaded DFFE in accordance withexamples of the present disclosure.

FIG. 15 depicts a three-stage DFFE with DFE outputs as initial tentativedecisions in accordance with examples of the present disclosure.

FIG. 16 depicts a three-stage DFFE in accordance with examples of thepresent disclosure.

FIG. 17 depicts a single-stage DFFE for a cascaded DFFE in accordancewith examples of the present disclosure.

FIG. 18 is a flow diagram illustrating an example of a method inaccordance with some embodiments.

DETAILED DESCRIPTION

The following disclosure provides many different embodiments, orexamples, for implementing different features of the provided subjectmatter. Specific examples of components and arrangements are describedbelow to simplify the present disclosure. These are, of course, merelyexamples and are not intended to be limiting. For example, the formationof a first feature over or on a second feature in the description thatfollows may include embodiments in which the first and second featuresare formed in direct contact, and may also include embodiments in whichadditional features may be formed between the first and second features,such that the first and second features may not be in direct contact. Inaddition, the present disclosure may repeat reference numerals and/orletters in the various examples. This repetition is for the purpose ofsimplicity and clarity and does not in itself dictate a relationshipbetween the various embodiments and/or configurations discussed.

Further, spatially relative terms, such as “beneath,” “below,” “lower,”“above,” “upper” and the like, may be used herein for ease ofdescription to describe one element or feature's relationship to anotherelement(s) or feature(s) as illustrated in the figures. The spatiallyrelative terms are intended to encompass different orientations of thedevice in use or operation in addition to the orientation depicted inthe figures. The apparatus may be otherwise oriented (rotated 90 degreesor at other orientations) and the spatially relative descriptors usedherein may likewise be interpreted accordingly.

Examples described herein are directed to a digital signal processing(DSP) Serializer/Deserializer (SerDes) receiver architecture thatincludes a Decision Feedforward Equalizer (DFFE) and equalization andclock data recovery (CDR) modules integrated with joint auto adaptationin such a way that the signal is optimally shaped for improved CDR andSerDes performance. Serdes is a device commonly used in high speedcommunications to compensate for limited inputs and outputs. A SerDesdevice converts data between parallel interfaces and serial interfaces,using one or more differential lines to transmit data from point A topoint B.

FIG. 1 depicts a block diagram of a SerDes communication system 100 inaccordance with examples of the present disclosure. More specifically,the SerDes system 100 includes a transmitter 104 communicatively coupledto a receiver 112 via a communication channel 108. The transmitter 104is configured to send one or more signals through the communicationchannel 108 to the receiver 112. The transmitter 104 may include one ormore finite impulse response filters for conditioning data beforetransmission to the communication channel 108. The communication channel108 may be a physical transmission medium, such as a backplane, drivehead in a magnetic recording system, copper cables, optical fibers, oneor more coaxial cables, and/or wire, or the communication channel 108may include a one or more radio frequency (RF) channels. Althoughdescribed herein as being utilized in a SerDes communication system 100,examples of the present disclosure are not so limited, and some examplesmight be employed in alternative communications systems utilizing atransmitter and a receiver communicating over a communication channel.Moreover, it is understood that each “bit” of a signal has acorresponding logic value and that various signals described herein mayutilize multi-bit data symbols based on various data encoding schemes,such as pulse amplitude modulation (e.g., PAM-4).

The effect of Inter-Symbol Interference (ISI) generally increases as thetransmission speed in the channel 108 increases. ISI is a form ofdistortion of a signal in which one symbol interferes with subsequentsymbols. This is an unwanted phenomenon as the previous symbols have asimilar effect as noise and therefore make the communication lessreliable. That is, the spreading of a pulse representing one or moreportions of a communication beyond its allotted time interval causes itto interfere with neighboring pulses. ISI is usually caused by multipathpropagation or the inherent linear or non-linear frequency response of acommunication channel causing successive symbols to “blur” together.Therefore, the presence of ISI in a communication system may introduceerrors that propagate to receiver output. Accordingly, a design oftransmitting and receiving filters generally minimizes the effects ofISI, and thereby delivers digital data to its destination with thesmallest error rate possible.

Traditional SerDes architectures are generally limited by the couplingissue between CDR and equalization adaptation. If CDR and equalizationare both adapted from a final equalized node, then the pulse response isideally flat due to equalization; however such a flat pulse responsemakes it difficult for baud-rate CDRs that are typically used in sucharchitectures to find a stable locking point since multiple points onthe pulse response satisfy the convergence criterion. To mitigate thisissue, CDR and equalization are adapted using different nodes, where theCDR uses a partially equalized node. This may potentially decouple CDRand equalization to avoid the fully equalized joint adaptation issue butthe pulse response at the partially equalized CDR node may not besymmetric which may lead to a sub-optimal CDR locking point. Even if theCDR convergence point is optimal relative to the partially equalized CDRnode, the CDR convergence point may not be optimal relative to the fullyequalized final node. Thus, the traditional SerDes architecturetypically requires CDR locking point adjustment mechanisms to achievebetter margins which adds to the complexity of the overall architecture.The CDR locking point and the BER margins tend to be sensitive to thetransmitter settings since they play a big role in determining the shapeof the pulse response and as such link tuning becomes a much harderexercise. Furthermore, since DFE is limited to postcursor ISI alone,equalization tends to be dominated by FFE which makes it more sensitiveto noise and crosstalk. Accordingly, limitations in traditional SerDesarchitecture include but are not limited to the following: the couplingbetween the CDR and equalization which leads to unsafe CDR convergencepoints; a pulse response that may not be symmetric at the CDR node whichleads to a sub-optimal CDR locking point; traditional SerDesarchitecture typically require CDR locking point adjustments for bettermargins; link margins of traditional SerDes architectures are sensitiveto transmitter settings and link tuning tends to be a non-trivialexercise.

FIG. 2 depicts an example SerDes receiver architecture 200 that includesan equalization data path for achieving both precursor and postcursorISI correction through a combination of a Feed-Forward Equalizer (FFE),Decision Feedback Equalizer (DFE), and a precursor tap enabled multi-tapDecision Feed-Forward Equalizer (DFFE). The SerDes receiver architecture200 may be implemented in the receiver 112, and as illustrated in FIG.2, may include an Analog Front End (AFE) 204 that includes one or moreof a Continuous Time Linear Equalizer (CTLE) 208 and a Variable GainAmplifier (VGA) 212. Since a serial-data channel tends to attenuatehigher frequencies of a signal more than lower frequencies of thesignal, the CTLE 208 is included to boost high frequencies of a receivedsignal 202 received at the SerDes receiver architecture 200 in order tobring a majority of the frequency components of the received signal 202to a similar or same amplitude. However, by boosting signal frequencies,jitter and noise are also boosted. The VGA 212 may be included tovariably boost signal amplitudes of the signal across the majority offrequencies. Accordingly, the AFE 204 generally minimizes ISI introducedby the combined characteristics of the transmitter and channel, such asISI due to the channel's impulse response, thereby reducing ISI at thereceiver.

The AFE 204 may provide the equalized signal to the analog to digitalconverter (ADC) 216 to convert the received and equalized signal into adigital signal for subsequent digital signal processing at a digitalsignal processor (DSP) 218. The DSP may include, but is not limited to aFFE 220, a clock data recovery (CDR) adaptation 224, a DFE 228, a DFFE232, and an equalization adaptation 236. More specifically, the CDRadaptation 224 may tap an intermediate node in the equalization datapath between the DFE 220 and the DFE 228 for reduced latency which leadsto improved jitter tracking performance. The joint adaptation (e.g., CDRadaption 224 and Equalization adaptation 236) that is implemented aspart of the SerDes receiver architecture 200 resolves potential negativeinteraction mechanisms between CDR adaptation 224 and equalizationadaptation 236. That is, the unique combination of equalization providedby the SerDes receiver architecture 200 together with the CDR adaption224 realizes a symmetric pulse response at the CDR node that's optimalfor Mueller-Muller baud-rate CDR. Mueller-Muller CDR, sometimes referredto as MM CDR, is a common and popular type of baud rate CDR. As theMM-CDR is typically sensitive to the shape of the pulse response, theproposed SerDes receiver architecture 200 addresses this limitation by“pulse shaping” the signal to be symmetric irrespective of the actualchannel pulse response. The MM-CDR also suffers from issues related tofinding a stable locking point when locking to a fully equalized nodesince every point on the pulse response can be a potential lockingpoint. However, the proposed SerDes receiver architecture 200 addressesthis issue by introducing residual ISI symmetrically with first tappostcursor ISI equal to first tap precursor ISI. This ensures a stableCDR convergence point with improved timing margins. The residual ISI isfully compensated by the final equalization stages and therefore doesnot impact the final bit-error-rate (BER) of the fully equalized signalthat is used for making decisions. Furthermore, the SerDes receiverarchitecture 200 has improved performance in the presence of noise andcrosstalk when compared to a traditional FFE dominant architecture dueto the additional use of the DFFE 232 for both precursor and postcursorISI correction. The SerDes receiver architecture 200, as presentedherein, achieves robust performance with BER improvement overtraditional architectures across a wider range of transmitter settingsas it is largely insensitive to the channel pulse response by virtue ofits CDR pulse shaping capability.

Unlike traditional SerDes architectures, in the SerDes receiverarchitecture 200, the DFE 228 may not be part of the main signal datapath. That is, in the equalization data path 221 as shown in FIG. 2, thesignal equalized by the DFFE 232 is actually the output of the FFE 220.The DFE 228 merely provides a first set of tentative decisionscorresponding to the FFE 220 output for the DFFE 232 to process. Thus,the DFE 228 may be omitted in some implementations. The DFE 228 may beused to start with a good BER at the input of the DFFE 232. If the DFE228 is bypassed, additional DFFE 228 stages, for example as depicted inFIG. 5, may be used to achieve a desired BER. In principle, the DFE 228can be bypassed and its usage can be determined by implementation costtradeoffs.

Similar to the DFE 228, the FFE 220 also may be omitted in someembodiments. The FFE 220 provides additional pre-equalization such thata signal starts off with a better SNR which provides a better BER oftentative decisions requiring fewer DFFE stages overall. The FFE 220 mayboost noise which can be addressed by removing the FFE 220 completely;however, additional DFFE stage(s) may be used to achieve a desired BERwhen the FFE 220 is not included in the architecture 200.

In accordance with examples of the present disclosure, the SerDesreceiver architecture 200 provided in FIG. 2 taps, or utilizes, the FFE228 node for CDR which has the benefit of having sufficient equalizationto reduce CDR noise and lower latency to improve jitter tracking.Accordingly, the CDR adaptation 224 is decoupled from the Equalizationadaptation 236 in principle since they are tapped from different nodes;that is, the CDR adaptation 224 utilizes the FFE 220 while theEqualization Adaptation 236 utilizes the DFFE 236. Accordingly, theSerDes receiver architecture 200 has the ability to adapt precursor andpostcursor ISI correction at both the intermediate CDR FFE node, forexample the FFE node 220, and the final equalized DFFE node, forexample, the DFFE node 232. As will be explained later, thisimplementation provides the flexibility to shape a symmetric pulseresponse at the CDR node 224, irrespective of the transmitter settings,utilizing residual ISI of both precursor and postcursor taps 220, 232fully compensated by follow-on DFFE stages. Since the SerDes receiverarchitecture 200 utilizes a multi-tap DFFE 232 topology with precursortaps, precursor ISI along with postcursor ISI at the CDR node 224 may beutilized so that the pulse response is symmetric and optimized forMM-CDR.

The DFFE 232 removes residual ISI present at the CDR node 224 since theDFFE 232 has the ability to correct both precursor and postcursor ISI.Furthermore, since significant equalization of the signal occurs afterthe FFE 228 with tentative decisions based on the DFFE 232, the SerDesreceiver architecture 200 is not FFE dominant and performs better in thepresence of noise and crosstalk than a traditional FFE dominantarchitecture. Robust performance is observed with orders of BERimprovement over traditional architecture due to the factors listedabove. In summary, the SerDes receiver architecture 200 may optimizepulse shaping for MM-CDR; reduce latency and improve jitter tracking asa result due to CDR tapping from an intermediate node in theequalization data path; reduce and/or eliminate coupling issues betweenCDR adaptation and equalization adaptation; provide a wider operatingrange of SerDes settings; require no special CDR locking pointadjustment, improve crosstalk performance over FFE dominant SerDesarchitectures; and provide a robust performance while improving BER overtraditional SerDes architectures.

The CDR pulse shaping features achieved via the SerDes receiverarchitecture 200 discussed above are further illustrated with referenceto FIGS. 3-4C. In accordance with the present disclosure, references toMM CDR and baud date CDR are meant as references to the phase errordetector (PED) that is used in a CDR loop 224 and not to be confusedwith the entire signal processing loop as a whole. For example, a PEDmay compare a phase between input data and a recovered clock and provideinformation to adjust a sampling clock's phase. While the presentdisclosure primarily focusses on MM-CDR, details discussed herein may begeneralized to other baud-rate CDRs since they share similar convergenceproperties.

MM CDR timing recovery may be explained using a pulse response as shownin FIG. 3. The first precursor 304, the main cursor 308, and the firstpostcursor 312 are represented in FIG. 3 by h(τ_(k)−T_(b)), h(τ_(k)) andh(τ_(k)+T_(b)) respectively, which may also be referred to utilizing amore simple notation h⁻¹, h₀ and h₁ respectively. The clock phaseconditions may be written as h⁻¹=h₁ (locked condition); h⁻¹<h₁ (earlycondition); and h⁻¹>h₁ (late condition). An optimal scenario for MM CDRis to lock at the peak of the pulse response, h₀, and because thelocking condition is given by h⁻¹=h₁, an optimal pulse response at theCDR node is a symmetric pulse response with an initial condition ofh⁻¹=h₁. For a given asymmetrical pulse as shown in FIG. 4A having aninitial h⁻¹ <h₁ and FIG. 4B having an initial h⁻¹>h₁, the CDR lockslater or earlier than the given peak of the response, respectively, toensure residual h⁻¹=h₁ leading to a lower h₀ after CDR convergence whichultimately results in lower margins.

However, for an ideal square wave pulse response with h⁻¹=h₁=0 as shownin FIG. 4C, MM CDR has an unstable locking point as any point on thepeak of the pulse response is a potential convergence point. This is dueto the fact that even if CDR moves early or late, the CDR convergencecriterion is met as long as the CDR is sampling the peak of the pulseresponse. MM CDR, in effect, can be considered to be a peak detectorsimilar to other baud rate CDRs; however, since a square wave pulseresponse has multiple peaks, it is actually not an optimal pulseresponse for MM CDR even though jitter and noise may result in a wideopen eye. Such a scenario may be encountered when a fully equalized nodeis sampled with MM CDR. Thus, an ideal node for MM CDR has partialequalization with residual h⁻¹=h₁.

FIG. 5 depicts a SerDes receiver architecture 500 illustrating furtheraspects of the SerDes receiver architecture 218 of FIG. 2 in accordancewith examples of the present disclosure. The SerDes receiverarchitecture 500 may initially receive, from an ADC, such as the ADC216, a digital signal y_(k). The digital signal y_(k) may be provided toan FFE 502, where the FFE 502 may be a finite impulse response (FIR)filter that can correct both precursor ISI and postcursor ISI. From theFFE 502, a precursor ISI and postcursor ISI corrected signal may proceedto a junction 504 where it may be combined with a compensated postcursorISI signal provided from a tentative decision slicer 506 and DFE FIR 508to generate a further compensation signal. The signal provided to andequalized by a DFFE, such as DFFE 510, may be the output of an FFE, suchas FFE 502. The DFE FIR 508 provides a first set of tentative decisionsfrom the tentative decision slicer 506 corresponding to the FFE 502output for the DFFE 510 to process. The DFE FIR 508 may be used toprovide an initial BER at the input of the DFFE 510. In some instances,the DFE 508 may be bypassed or otherwise not utilized; in suchinstances, additional DFFE 510 stages, such as DFFE 512, DFFE 514, maybe implemented to achieve a desired BER at the final output.

From the multistate multi-tap DFFEs 510-514, error may be determined atjunction 516 based on target levels 518. While DFFEs 510-514 areillustrated in FIG. 5, more or fewer DFFEs may be utilized. As furtherdepicted in FIG. 5, one or more least mean square LMS coefficients 520may be derived from the error and data provided by the DFFE 514; the oneor more LMS coefficients 520 may be provided back to each of the DFFE510-514. Moreover, LMS coefficients 522 and/or 524 may be provided tothe DFFE FIR 508 and FFE 502. A CDR adaption may occur at 528 and may beprovided back to the ADC, such as ADC 216. Additional details of a DFFEare provided in FIGS. 9-10 in accordance with examples of the presentdisclosure.

FIG. 6 provides additional details of an example of the FFE 502 inaccordance with examples of the present disclosure. More specifically,the FFE 502 may be a finite impulse response (FIR) filter that maycorrect both precursor ISI and postcursor ISI. As depicted in FIG. 6, ablock diagram depicts an FFE for one symbol with ‘m’ precursor taps(602A-602D) and ‘n’ postcursor taps (604A-604D), as well as a pluralityof unit delays 606. The unit delays 606, for example z⁻¹, required forFFE implementation may be implemented in a DSP SerDes architecture suchas the SerDes receiver architecture 200 within the digital domain. Whilethe FFE can provide a high frequency boost to compensate for channelloss, correct both precursor ISI and postcursor ISI, and provide aparallel data path implementation, the FFE may amplify crosstalk andnoise and may be cost prohibitive to implement when multiple taps may berequired. However, the FFE 502 may provide an initial signal to the CDRand follow-on equalization stages. An initial signal, x_(k), may beinput, where one or more precursor signal components derived from theprecursor taps 602A-602D and delayed by z⁻¹ for example, and one or morepostcursor signal components derived from the postcursor taps 604A-604Dand delayed by z⁻¹ for example, may be provided to a summation component608. The FFE 502 may output the signal x_ffe_(k).

FIGS. 7A-7C depict additional details of DFE implementations,corresponding to the DFE 508, decision slicer 506 and junction 204 shownin FIG. 5, in accordance with examples of the present disclosure. Morespecifically, a DFE, such as DFE 508, is a filter that may use feedbackof detected symbols to produce an estimate of an output, such as achannel output. Detected symbols are input to the DFE, such as DFE 508,such that the DFE produces an output which may be subtracted from theoutput of a linear equalizer if one is present. The DFE, such as DFE508, may correct postcursor ISI, as depicted in FIG. 4B for example, byincluding a FIR filter in a feedback loop using actual decisions from adecision slicer. Since DFE uses past decisions in a feedback path, DFEcan only correct postcursor ISI associated with those symbols. DFE doesnot have the ability to correct precursor ISI as that requires theknowledge of future samples.

FIG. 7A illustrates a block diagram of a DFE in a ‘direct feedback’configuration. That is, a signal y_(k), may be provided to a summationjunction 702; the signal resulting from the summation junction 702 isprovided to the decision slicer 704, where the decision slicer 704 makesa symbol decision. The decision slicer 704 quantizes the input such thatthe ISI may be directly subtracted from the incoming signal y_(k) viathe feedback FIR filter 706.

Some topologies of DFE pre-calculate decisions speculatively and chooseone of the pre-calculated decisions based on past symbols in order toeliminate the feedback path at the decision slicer 704. For example, ablock diagram of a 1-tap speculative DFE is illustrated in FIG. 7B forNRZ signaling and FIG. 7C for PAM4 signaling. The 1-tap speculative DFEillustrated in FIG. 7B includes summing junctions 708 and 710, decisionslicers 712 and 714, a multiplexor 716 and a latch or flip flop 718. Thenumber of slicers for 1-tap DFE may be doubled for PAM4 over NRZ alongwith the change of associated multiplexor to 4-to-1 from 2-to-1 asdepicted in FIG. 7C. That is, the number of slicers 720 fed by inputs722 may be doubled over the NRZ signaling of FIG. 7B, requiring amultiplexor 724 with additional inputs providing a selected signal tothe flip flop 726.

In accordance with examples of the present disclosure, a configurationof iterative Decision Feedforward Equalizer using tentative decisions ispresented herein that is less complex than multitap DFEs to implementand achieves both multi-tap precursor and postcursor ISI correction.Tentative decisions may be used such that multiple iterations improvethe quality of the tentative decisions.

FIG. 8 illustrates further aspects of a DFFE, such as the DFFE 510 ofFIG. 5, in accordance with some examples. More particularly, FIG. 8depicts a basic iteration stage of a multi-tap DFFE configuration 800with ‘m’ precursor and ‘n’ postcursor taps. The multi-tap DFFEconfiguration depicted in FIG. 8 does not suffer from noise or crosstalkenhancement as FFE does since DFFE uses decision outputs of slicers asinputs to the FIR unlike FFE which uses actual analog signal inputs. Thedigital outputs of the tentative decision slicers are multiplied withthe tap coefficients to reduce an amount of noise. Further, sincedigital outputs are used as the multiplier inputs, the multipliers ineffect get turned into adders which tend to be easier to implement. Morespecifically, a signal x_(k) may be input to precursor taps 804A-D, thecursor tap 804E, and the post cursor taps 804F-I (collectively taps 804)and may be delayed at each tap 804 by an amount z⁻¹ as shown in delayelements 806. Each of the taps 804 are then fed to a tentative decisionslicer 808. Each of the outputs from the tentative decision slicers 808may be provided to multipliers 812, where each multiplier 812 multipliesthe result of the tentative decision slicer 808 by a coefficient. Forexample, the tentative decision slicer 808 may quantize the sampledinput from the filter taps 804A-804I, where the quantized value may bescaled by a filter tap coefficient provided at the multipliers 812. Eachof the outputs from the multipliers 812 may be provided to an adder, orcombiner 816, where each of the outputs are effectively subtracted fromthe cursor tap 804E, providing an output that is precursor andpostcursor ISI compensated.

The mathematical block diagram of single stage DFFE 902, correspondingto the example DFFE 510 of FIG. 5, is illustrated in FIG. 9. Aspreviously mentioned, the decisions at the first slicer 904 output areonly tentative which are then used in the FIR filter 906 to equalize thesignal at the junction 908, which is then input to the next stageslicers, such as slicer 910. The bit-error-rate (BER) of the final stagedecisions, such as 910, can be shown to be lower or better than the BERof the previous stage tentative decisions, such as 904 for example. Thisproperty of DFFE may be used to cascade multiple stages and lower theBER to the desired level with each successive iteration. The lower thestarting BER, the fewer the required stages of DFFE. Furthermore, sincedecisions are tentative and used as inputs in a feedforward path asopposed to the feedback path of DFE, DFFE does not suffer from errorpropagation. More importantly, the complexity of the DFFE scaleslinearly with the number of taps and thus it is feasible to implementmulti-tap DFFE for both precursor and postcursor ISI in a DSP SerDesarchitecture. Accordingly, higher order floating taps may be implementedto handle non-ideal channel behavior such as reflections. Advantages ofDFFE include ISI cancellation with no crosstalk or noise enhancement; animplementation complexity that scales linearly with the number of taps;a parallel data path DSP implementation; reduced or no error propagationas exhibited by DFE; reduced or no critical feedback path timingchallenges as seen in DFE; and the multipliers of FFE may be replaced byadders in DFFE.

It can be the shown that the quality of the decisions at the outputslicers, such as output slicer 910 for example, is better than thequality of the tentative decisions at the preceding stage slicers, forexample tentative decisions from the decision slicer 904. The reason isthat when the first stage slicers, such as slicers 904 for example, makethe correct tentative decisions, the output stage slicers, such asslicer 910, also make the correct decisions with an increased margin.However, when the tentative decisions, from slicer 904 for example, areincorrect, the output stage slicers, such as slicer 910, doesn't alwaysmake incorrect decisions. That is, the final stage decisions may becorrect even when the tentative decisions are in error since wrongtentative decisions can, in some instances, provide helpful ISIcompensation even if it is technically incorrect. This is because theISI is actually helpful when there are no transitions in the datapattern. For example, for a data pattern of D_(k-1)=D_(k) the ISI from aD_(k-1) symbol improves the signal levels for detecting a D_(k) symbol.Further, when D_(k-1) is in error for such a pattern, the ISIcompensation corresponding to the incorrect D_(k-1) helps in restoringthe signal for the D_(k) symbol. For example, a simplified analysis isprovided below:

Consider NRZ data transmission on a channel whose pulse response has amain cursor of h₀ and a first tap postcursor of h₁. The signal level,X_(k), corresponding to the D_(k) bit is provided in Equation 1.

X _(k) =h ₀·sgn(D _(k))+h ₁·sgn(D _(k-1))  Equation 1

The output signal level, Y_(k), corresponding to the D_(k) bit after ISIcompensation with a correct detection of D_(k-1) is given by Equation 2:

Y _(k) =h ₀·sgn(D _(k))+h ₁·sgn(D _(k-1))−h1·sgn(D _(k-1))=>Y _(k) =h₀·sgn(D _(k))  Equation 2

However, when there is an error in detection of D_(k-1), the signallevel, Y_(k), corresponding to the D_(k) bit after ISI compensation withan incorrect tentative decision is given by Equation 3:

Y _(k) =h ₀·sgn(D _(k))+h ₁·sgn(D _(k-1))+h ₁·sgn(D _(k-1))=>Y _(k) =h₀·sgn(D _(k))+2h1·sgn(D _(k-1))  Equation 3

But when D_(k-1)=D_(k), the signal level, Y_(k)′, after incorrecttentative decision of D_(k-1) is actually positively restored for thecorrect detection of D_(k) bit as given by Equation 4:

Y _(k) =h ₀·sgn(D _(k))+2h ₁·sgn(D _(k))=>Y _(k)=(h ₀+2h ₁)·sgn(D_(k))  Equation 4

It can therefore be seen that is a lower chance of error even when theprevious decision is incorrect. By extending the above analysis, we canconclude that in the DFFE topology as shown in FIGS. 8 and 9, the BER offinal stage slicers, D_(k) ¹, is lower than the BER of initial stageslicers, D_(k) ⁰.

The probability of error detection can be expressed as:

P _(e)(D _(k) ¹)=P _(e)(D _(k) ⁰)·P _(e)(D _(k) ¹ ,D _(k) ⁰|e=1)  Equation 5

where P_(e)(D_(k) ¹) stands for the probability of error in D_(k) ¹ andP_(e)(D_(k) ¹,D_(k) ⁰|e=1) stands for the probability of error in D_(k)¹ when there is an error in D_(k) ⁰. From the above equation, we can seethat P_(e)(D_(k) ¹)<P_(e)(D_(k) ⁰)=>BER(D_(k) ¹)<BER(D_(k) ⁰). Thisproperty of DFFE can be can be used to cascade multiple stages of DFFEand progressively lower the BER of each iteration until we reach thedesired BER level or until we reach a stage where no further BERreduction is possible due to SNR being limited by noise and not ISI. Ablock diagram for a 2-stage DFFE 1002 is shown in FIG. 10. Morespecifically, a first stage 1004 may include a tentative decision slicer1006 which provides tentative decision to a first FIR filter 1008. Anequalized signal from the first junction 1010 may be provided to thesecond stage 1012, which includes a decision slicer 1014, which can beconsidered a tentative decision slicer. The quantized decisions from thedecision slicer 1014 may be provided to a second FIR filter 1016. Theequalized signal resulting from the second junction 1018 may be providedto the decision slicer 1020.

The BER relations of each stage can be expressed as follows

BER(D _(k) ²)<BER(D _(k) ¹)<BER(D _(k) ⁰)  Equation 6

The above equation be generalized and extended for multiple stages.

In accordance with examples of the present disclosure, the decisionslicers, such as decision slicers 904 and/or 910, are inherentlynon-linear in nature but based on some simplifying assumptions, a linearmodel for the purposes of analysis can be built. One potentialdisadvantage of using decision slicers, such as decision slicers and/or910, is that the decision slicers block the noise from passing throughand thus the slicer can be considered to be an open circuit for noiseanalysis. It is evident that there is no noise enhancement due to theuse of slicers in the FIR and thus for this analysis, the signalequalization case can be considered.

In a fully equalized case, the signal levels before and after theslicers are at their corresponding logic amplitude levels. Thus theslicer can be considered as a short for such cases. To be more accurate,one can use a scaling factor of α; but for the purposes of thisanalysis, α=1.

Considering an ideal feedback equalizer with ‘m’ precursor and ‘n’postcursor taps, the equation for such an equalizer is given by Equation7:

y _(k) =x _(k)−Σ_(i=−m) ^(i=n) h _(i) ·D _(k-i) ,i≠k  Equation 7

This is similar to a DFE except that the above equation includesprecursor tap correction as well, whereas DFE is limited to postcursorISI correction only. It also has to be noted that there is no practicalway to realize the above equalizer since it requires the use of futuresymbols. This analysis is simply to compare the performance of DFFE withsuch an ideal equalizer.

Thus, a linearized model for such an ideal feedback equalizer is shownin FIG. 11. The FIR 1102 in the feedback path of this ideal equalizer issimilar to the FIR shown in FIGS. 5 and 7A and is given by Equation 8:

FIR=Σ_(i=−m) ^(i=n) h _(i) ·z ^(−i+m) ,i≠0  Equation 8

The transfer function of this ideal equalizer, Ideal_Feedback_Eq(z),then follows from the linear model of FIG. 7A as shown below in Equation9:

Ideal_Feedback_Eq(z)=1/(1+FIR)  Equation 9

Using Taylor series expansion, the above equation can be expressed asEquation 10:

Ideal_Feedback_Eq(z)=1−FIR+FIR²−FIR³+FIR⁴ . . .  Equation 10

Now, considering the linearized model of DFFE (such as the DFFE 510 ofFIG. 5) which is shown in FIG. 12, the transfer function of DFFE,DFFE(z), can be expressed as DFFE(z)=1−FIR. Accordingly, the DFFEtransfer function lacks the higher order terms of the ideal equalizer.However, by cascading multiple DFFE stages, each higher order term canbe realized with every additional iteration stage. For example, alinearized model of a 2-stage DFFE as shown in FIG. 13, includes a firststage 1302 and a second stage 1304. The transfer function of a 2-stageDFFE, DFFE2(z), is given by Equation 11:

DFFE2(z)=1−FIR·(1−FIR)=>DFFE2(z)=1−FIR+FIR²  Equation 11

Similarly, the transfer function of a 3-stage DFFE, DFFE, DFFE2(z), isgiven by Equation 12:

DFFE3(z)=1−FIR·(1−FIR+FIR²)=>DFFE3(z)=1−FIR+FIR²−FIR³  Equation 12

The analysis can be extended to show that the higher order terms of anideal equalizer can be realized by adding corresponding stages of DFFE.For a practical application with a reasonable starting SNR, the DFFE canachieve within first few iterations the same performance as that of anideal feedback equalizer even with precursor taps. But a benefit of DFFEis that while the ideal feedback equalizer is not implementable, DFFE iseasy to implement even with the inclusion of precursor taps.

DFFE, such as the DFFE 510 of FIG. 5, is an iterative equalizer whichcan be cascaded multiple times to realize a higher order DFFE. To builda higher order multi-tap DFFE, the multi-tap DFFE in a single stageDFFE, such as that depicted as DFFE 800 in FIG. 8, may be modified toprovide the DFFE 1400 as illustrated in FIG. 14, by separating thecursor path 1402 from the precursor taps 1404 and postcursor taps 1406.Accordingly, the cursor from the cursor path 1402 is provided to eachsubsequent stage unaltered from the previous stage. For example, thecursor path 1502 may be provided to the first stage 1504, second stage1508, and third stage 1512. Returning to FIG. 14, the precursor taps1404 and postcursor taps 1406 may be provided to the tentative decisionslicers 1408 of the instant DFFE, scaled and summed at the junction 1410to be provided as an output. As depicted in FIG. 15, the output 1506from the first stage 1504 is provided to the second stage 1508 and theoutput 1510 from the second stage 1508 is provided to the third stage1512. Thus, by cascading three single stage DFFE modules as shown inFIG. 15, a third order DFFE may be realized.

The number of DFFE stages required may be a function of the BER of theinitial decisions. The better the BER at the outset, the fewer the DFFEstages may be required. To improve the quality of the initial tentativedecisions, DFE slicer outputs may be used instead of raw slicer outputsdepicted in FIGS. 14 and 15. That is, a 3-stage DFFE 1600 as shown inFIG. 16 uses DFE outputs 1602 as initial tentative decisions in thefirst stage 1604. To accommodate the DFE slicer outputs 1602, the singlestage DFFEs 1604, 1608, and 1612 have been modified to take decisions asinputs by utilizing slicers external to the DFFEs 1604, 1608, and 1612.The use of this cascaded DFFE configuration, such as the 3-stage DFFE1600 as shown, not only eliminates residual ISI but also enablesoptimized pulse shaping for MM CDR that leads to robust performance withless sensitivity to SerDes tuning. Accordingly, a single stage of theDFFE 1600, such as the DFFE 1604, 1608, and/or 1612, is depicted as aDFFE 1700 in FIG. 17. The DFFE 1700 is similar to the DFFE 1400 of FIG.14 but differs in that the decision slicers 1408 of the DFFE 1400 arenot included within the DFFE 1700. That is, decision slicers, such asdecision slicers 1606 and 1610, are external to the DFFEs 1604 and 1608respectively, as depicted in FIG. 16. The DFFE 1700 still separates thecursor path 1702 from the precursor taps 1704 and postcursor taps 1706.

One of the biggest challenges of integrating MM CDR with equalizationblocks in SerDes is to determine a joint adaptation solution thatresolves undesired coupling mechanisms between CDR and equalizationadaptation. The proposed SerDes receiver architecture 500 with itsunique combination of CDR, equalization and joint adaptation not onlyresolves any unwanted coupling between CDR and equalization adaptationbut the architecture also shapes the pulse response at the CDR node insuch a way that it's optimal for MM CDR and overall SerDes margins.

The adaptation of equalization blocks such as FFE, DFE and DFFE istypically implemented using least mean squares (LMS) algorithm thatminimizes the error power of the signal when compared to the targetequalized signal levels. The goal of the adaptation of equalization tapcoefficients is to eliminate any residual ISI at those tap positions.This discussion will focus on h−1 and h1, the first precursor tap ISIand first postcursor tap ISI respectively, since MM CDR is impactedprimarily by them. The locking condition for MM CDR is given by h−1=h1.The MM CDR PED, listed here just for completeness, is implemented usingsignal level y(k) based PED equation of Equation 13:

(k−1)·[k]−(k)·[k−1]  Equation 13

or error e(k) based PED equation of Equation 14:

[k−1]·[k]−[k]·[k−1]  Equation 14

To overcome coupling issues between CDR and equalization, varioustechniques have been used in the past such as introducing residual ISIat the CDR node; however, such techniques affect the cost of impactingoverall margins and tuning complexity regarding how much residual ISI tointroduce. The proposed SerDes receiver architecture 500 addresses thesecoupling issues by having CDR tapped from an intermediate node in theequalization data path and follow on equalization stages that compensateboth precursor and postcursor ISI. For example, returning to FIG. 5, theCDR 526 is tapped between the FFE 502 and junction 504, while theequalization stages including DFFE 510, DFFE 512, and DFFE 514,compensate for both precursor and postcursor ISI. Coupled with theability to add or subtract ISI at both the CDR 526 and final equalizednodes provides a pulse response at the CDR node 526 in a way that isoptimal for MM CDR but without any residual ISI at the final equalizednode.

Attributes of the proposed SerDes receiver architecture that ensureoptimized CDR pulse shaping are summarized below. More specifically, theCDR is tapped from the FFE node 526 for example and followed by one ormore DFFEs, such as DFFEs 510, 512, and 514) having the ability tocompensate both precursor ISI (h⁻¹) and postcursor ISI (h₁) such that MMCDR PED is used with a convergence condition of h⁻¹=h₁. Moreover,adaptation is driven from the final equalized node; that is, LMSadaptation is used to drive both FFE and DFFE equalization. For example,as adaptation minimizes ISI at the FFE node utilizing the LMScoefficients 524 for example, the pulse response becomes more symmetricdriving MM CDR to a better convergence point; because the DFFEadaptation runs in parallel—providing LMS coefficients to the DFFEs 510,512, and 514 for example, the multistage DFFE eliminates residual ISIseen at the CDR node 526 which is symmetric in terms of h⁻¹ and h₁ byvirtue of MM CDR adaptation; and the net result is a symmetric pulseresponse at the CDR node 526 that is near optimal for MM CDR but withoutthe downside of residual ISI at the final equalized node.

For reliable convergence, the adaptation loop gain of CDR is typicallyset to be higher than that of FFE which is in turn set higher than thatof DFFE. Additional details of the CDR pulse shaping mechanism ashighlighted above is further explained below.

Equalization is shared between FFE and DFFE with adaptation driving boththeir LMS coefficients for example, in such a way that final ISI at theDFFE node is zero. That is, =>h⁻¹(DFFE)=0, h₁(DFFE)=0→driven by LMSadaptation.

This ensures that there is residual ISI at the FFE node which alsohappens to be the CDR node. The amount of the residual ISI at FFE node502 depends on the adapted FFE coefficients 524 and DFFE coefficients520 which in turn are determined by the relative loop gains of FFE andDFFE adaptation. With non-zero DFFE coefficients and final ISI at zero,there may be residual ISI at the FFE node 502 that DFFE compensated for.That is, =>h⁻¹(FFE)≠0, h₁(FFE)≠0→due to DFFE sharing adaption.

Since MM CDR is adapting in parallel, a lock condition occurs whereh⁻¹=h₁ at the CDR node 526. That is, =>h⁻¹(FFE)=h₁(FFE)→driven by MM CDR

Accordingly, there is a symmetric pulse response with non-zero ISI atthe FFE node 502 or CDR node 526 which is ensured by the jointadaptation of MM CDR, FFE and DFFE. That is, =>h⁻¹(FFE)=h₁(FFE)≠0→drivenby joint adaptation of MM CDR, FFE and DFFE.

This is an optimal condition for MM CDR. Even if the pulse responsebefore adaptation is asymmetric, the system converges with ISI beinginjected or removed at both the FFE node 502 (which is the CDR node 526)and the DFFE node (which is the final equalized node) in such a way thatthere is a symmetric pulse response with non-zero ISI at the CDR node526. In some cases, ISI is injected at the FFE node 502 to make thepulse response symmetric and to have the overall ISI to be zero.

The symmetric CDR pulse shaping can be leveraged to simplify adaptationand speed up overall system convergence by forcing h⁻¹ and h₁ DFFEcoefficients to be equal and adapting or fixing only one of them.

The advantage with this CDR pulse shaping procedure over previous CDRadjustment mechanisms using residual ISI is that the residual ISI at theCDR node 526 is fully compensated by the follow on DFFE stages 510, 512,and 514 with little to no impact to overall BER. Furthermore, theresidual ISI is introduced in a symmetric manner with h⁻¹=h₁, which isoptimal for MM CDR. Since the pulse response is largely symmetricregardless of the amount of residual ISI at the CDR node 526, CDR locksnear the peak of the pulse response and is less sensitive to convergedvalues which are determined by the relative adaptation loop gains.

Another benefit of having a symmetric pulse response at the CDR node 526exists. The CDR locking point is determined by the pulse response at theCDR node 526 and as such even if the CDR node locks to an optimal pointrelative to the eye at the CDR node 526, it is not necessarily optimalrelative to the eye at the fully equalized node, for example the outputof DFFE 514, thereby possibly reducing timing margins at the fullyequalized node, for example the output of DFFE 514, even if the ISI isfully compensated. However, with a symmetric pulse response at thepartially equalized CDR node 526, the optimal CDR locking point asdetermined by the partially equalized eye tends to be fairly close tothe optimal locking point relative to the fully equalized eye. This isbecause when the partially equalized eye is superposed over a fullyequalized eye, the zero crossing points are similar. This can beconcluded with a simplified analysis as shown below.

For a fully equalized eye, the zero crossing point is at half UI pointbefore or after the peak of the eye. For the partially equalized signalwith a symmetric pulse response, the pulse response value at half UIpoint before the peak for 0->1 transition can be approximated as shownin Equation 15:

p _(0.5) =h _(−0.5) →h _(0.5)(for 0→1 transition)  Equation 15

where p_(0.5) is the signal value at half UI point before the peak ofthe pulse, h_(−0.5) is the half UI precursor ISI value and h_(0.5) isthe half UI postcursor ISI value respectively. For a symmetric pulseresponse, we can consider h_(−0.5) to be equal to h_(0.5). Therefore, asprovided by Equation 16,

p _(0.5) =h _(−0.5) −h _(0.5)=0(for 0→1 transition).  Equation 16

Similarly, p_(0.5)=−h_(−0.5)+h_(0.5)=0 (for 1→0 transition).

Based on the above equations, the zero crossing points for the partiallyequalized eye and the fully equalized eye are at the same location whensuperposed over each other. Therefore, the optimal CDR locking pointsrelative to both the eyes are similar. This analysis is based onsimplified assumptions assuming there is no ISI impact beyond the firstprecursor and postcursor taps. However, since they are dominant ISIterms and CDR being primarily impacted only by them, the conclusions arestill valid.

While least mean square (LMS) based adaptation is disclosed herein, andwhile some embodiments may refer to least mean square (LMS)coefficients, coefficients derived by other means within the scope ofthe disclosure.

FIG. 18 is a flow diagram illustrating a method of generating data froman input signal received from a channel in accordance with someembodiments. The method could be implemented with the SerDes receiverarchitecture 500 shown in FIG. 5, though the illustrated method isapplicable to other architectures. Referring to FIG. 5 in conjunctionwith FIG. 18, at step 1810, samples are generated from the input signalwith a sampling module implemented by the FFE 502. At step 1812, atentative decision slicer 506 is applied to each of the generatedsamples, and the output of the tentative decision slicer is operated onutilizing one or more filter coefficients by one or more DFFEs 510, 512,514 at step 1814. At step 1816, the resulting output from the filter tapoperation is combined at a summing junction 516.

In one example, a decision feedforward equalizer (DFFE) is provided. TheDFFE may include a plurality of precursor taps configured to sample areceived signal by different time delay amounts, a plurality ofpostcursor taps configured to sample the received signal by differenttime delay amounts, and a cursor tap configured to sample the receivedsignal. Moreover, the DFFE may include a plurality of tentative decisionslicers configured to quantize outputs from the plurality of precursortaps and plurality of postcursor taps, and a summation elementconfigured to combined scaled outputs provided by the plurality oftentative decision slicers and the received sampled signal from thecursor tap.

In another example, a serializer/deserializer receiver including adecision feedforward equalizer (DFFE) is provided. The DFFE may includea plurality of precursor taps including a first precursor tap configuredto sample a received signal, and a second precursor tap configured tosample the received signal by a first delayed amount. The DFFE mayadditionally include a cursor tap configured to sample the receivedsignal by a second delayed amount and a plurality of postcursor taps.The plurality of postcursor taps include a first postcursor tapconfigured to sample the received signal by a third delayed amount, anda second postcursor tap configured to sample the received signal by afourth delayed amount. The DFFE may additionally include a plurality oftentative decision slicers that include a first tentative decisionslicer configured to receive the sampled signal from the first precursortap and provide a first quantized output to a first multiplier, a secondtentative decision slicer configured to receive the sampled signal fromthe second precursor tap and provide a second quantized output to asecond multiplier, a third tentative decision slicer configured toreceive the sampled signal from the first postcursor tap and provide athird quantized output to a third multiplier, and a fourth tentativedecision slicer configured to receive the sampled signal from the secondpostcursor tap and provide a fourth quantized output to a fourthmultiplier. The DFFE also may include a summation element configured tosubtract outputs from each of the first multiplier, the secondmultiplier, the third multiplier, and the fourth multiplier from thesampled signal provided by the cursor tap and provide the difference asan equalized output signal.

In another example, a method of generating data from an input signalreceived from a channel is provided. The method may include generatingsamples from the input signal with a sampling module, applying atentative decision slicer to each of the generated samples, operating onthe output of the tentative decision slicer utilizing one or more filtercoefficients, and combining the resulting output from the filter tapoperations.

The foregoing outlines features of several embodiments so that thoseskilled in the art may better understand the aspects of the presentdisclosure. Those skilled in the art should appreciate that they mayreadily use the present disclosure as a basis for designing or modifyingother processes and structures for carrying out the same purposes and/orachieving the same advantages of the embodiments introduced herein.Those skilled in the art should also realize that such equivalentconstructions do not depart from the spirit and scope of the presentdisclosure, and that they may make various changes, substitutions, andalterations herein without departing from the spirit and scope of thepresent disclosure.

What is claimed is:
 1. A method, comprising: inputting a signal toprecursor taps, a cursor tap, and post cursor taps; delaying the signalat each of the taps by a delay amount; providing, from an output of eachtap, the delayed signals to corresponding tentative decision slicers;quantizing the delayed signals with the tentative decision slicers togenerate quantized sampled signals; multiplying the quantized sampledsignals with tap coefficients to reduce noise; and combining themultiplied quantized sample signals to compensate precursor andpostcursor inter-symbol interference.
 2. The method of claim 1, whereinthe input signal comprises a non-equalized signal.
 3. The method ofclaim 1, wherein the input signal is received from a feedforwardequalizer.
 4. The method of claim 1, further comprising outputting anequalized signal based on the combined multiplied quantized samplesignals.
 5. The method of claim 4, further comprising: sampling theequalized signal by a second plurality of precursor taps; sampling theequalized signal by a second plurality of postcursor taps; sampling theequalized signal by the cursor tap; quantizing the sampled equalizedsignals; and combining the quantized sampled equalized signals.
 6. Themethod of claim 5, wherein the combined quantized sampled equalizedsignals have a bit-error-rate that is less than a bit-error-rate of thecombined multiplied quantized sample signals.
 7. The method of claim 1,wherein a number of postcursor taps is greater than a number ofprecursor taps.
 8. A decision feedforward equalizer (DFFE), comprising:a plurality of precursor taps configured to sample a received signal bytime delay amounts; a cursor tap configured to sample the receivedsignal by a time delay amount; a plurality of postcursor taps configuredto sample the received signal by different time delay amounts; aplurality of tentative decision slicers corresponding with outputs ofthe taps and configured to receive the delayed signals from the taps,and to quantize the delayed signals to generate quantized sampledsignals; multipliers configured to multiply the quantized sampledsignals with tap coefficients to reduce noise; and a summation elementconfigured to combine the multiplied quantized sample signals tocompensate precursor and postcursor inter-symbol interference.
 9. TheDFFE of claim 8, wherein a difference provided by the summation elementis an equalized signal.
 10. The DFFE of claim 9, further comprising: asecond plurality of precursor taps configured to sample the equalizedsignal.
 11. The DFFE of claim 10, further comprising: a second pluralityof postcursor taps configured to sample the equalized signal; the cursortap configured to sample the equalized signal; a second plurality oftentative decision slicers configured to quantize outputs from thesecond plurality of precursor taps and second plurality of postcursortaps; and a second summation element configured to combine scaledoutputs provided by the second plurality of tentative decision slicersand the sampled equalized signal provided by the cursor tap.
 12. TheDFFE of claim 11, wherein an output of the second summation element hasa bit-error-rate that is less than the output of the summation element.13. The DFFE of claim 8, wherein a number of postcursor taps is greaterthan a number of precursor taps.
 14. A serializer/deserializer,comprising: a decision feedforward equalizer (DFFE), comprising: tapsconfigured to receive an input signal, and to sample the input signal bytime delay amounts; tentative decision slicers configured to quantizethe time delayed samples; and a summation element configured to combinethe quantized time delayed samples to provide an output signal having adesired bit error rate (BER).
 15. The serializer/deserializer of claim14, wherein the DFFE further comprises: multipliers configured tomultiply the quantized time delayed samples with tap coefficients toreduce noise.
 16. The serializer/deserializer of claim 14, wherein thetaps comprise: a plurality of precursor taps configured to sample theinput signal by time delay amounts; a cursor tap configured to samplethe input signal by a time delay amount; and a plurality of postcursortaps configured to sample the input signal by different time delayamounts.
 17. The serializer/deserializer of claim 16, wherein a numberof postcursor taps is greater than a number of precursor taps.
 18. Theserializer/deserializer of claim 14, further comprising: an analog todigital converter (ADC) configured to receive an analog signal andoutput a digital signal; and a feed-forward equalizer (FFE) having aninput terminal connected to the ADC to receive the digital signal, theFFE configured to correct precursor Inter-Symbol Interference (ISI) andpostcursor ISI of the received digital signal, and to provide the inputsignal to the DFFE.
 19. The serializer/deserializer of claim 18, whereinthe FFE is configured to sample the digital signal delayed by differenttime delay amounts.
 20. The serializer/deserializer of claim 18, whereinthe FFE comprises: a cursor tap; a plurality of precursor taps; aplurality of postcursor taps; and a plurality of delay elementsconnected between the cursor tap, the plurality of precursor taps, andthe plurality of postcursor taps and the FFE input terminal.